Timeline for Characterisation of Sobolev spaces using their Lipschitz approximations
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Nov 9 at 14:11 | history | bounty ended | Nate River | ||
| S Nov 9 at 14:11 | history | notice removed | Nate River | ||
| Nov 9 at 6:02 | comment | added | Pietro Majer | Something similar should be true. As a general principle, the quicker the approximation of a function by regular functions converges, the more regular is the function, and conversely | |
| Nov 9 at 5:36 | vote | accept | Nate River | ||
| Nov 9 at 3:17 | comment | added | Nate River | @PietroMajer That would have been a very nice analogy if true... | |
| Nov 8 at 18:21 | comment | added | Pietro Majer | The (concave) modulus of continuity $\omega(t)$ of a uniformly continuous function $f$ on a bounded convex domain $C$ can be reconstructed from the distance from the $k$-Lipschitz functions $\delta(k):=\inf_{g\in \text{Lip}_k(C)}\|f-g\|_{\infty,C}$ (they are related by a Legendre transform). Maybe there is an analogous fact for integral norms? | |
| Nov 8 at 18:00 | answer | added | Justthisguy | timeline score: 1 | |
| S Nov 8 at 5:58 | history | bounty started | Nate River | ||
| S Nov 8 at 5:58 | history | notice added | Nate River | Draw attention | |
| Oct 27 at 2:07 | comment | added | JJJ | I think there is a 50% chance this is true. | |
| Oct 19 at 10:34 | comment | added | Nate River | “If” direction seems much harder. | |
| Oct 19 at 10:29 | comment | added | Nate River | Hm, “only if” should be true by the Kirzbaum-Valentine theorem… | |
| Oct 19 at 9:57 | history | edited | Nate River | CC BY-SA 4.0 |
added 8 characters in body
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| Oct 19 at 7:41 | history | asked | Nate River | CC BY-SA 4.0 |